When
reading the various discussions of nuclear binding energy by different
authors, it is easy to get confused because of an understood convention.
Binding energy is always negative.
When they talk about its magnitude,
they mean its absolute value, so they just state
the positive number.

You see,
the nuclear physicists (like many parts of physics) have been very sloppy
in definitions. E.g., here’s one definition advanced for nuclear binding
energy:

Binding
Energy:
The binding energy of a nucleus is the minimum energy required to
disassociate it into its
component neutrons and protons. Neutron and proton binding energies are
those required to remove a neutron or a proton, respectively, from a
nucleus. Electron binding energy is that
energy required to remove an electron from an
atom or a molecule.

From a
sheer logic standpoint, all three of those “definitions” are wrong. Restating
them correctly:

The absolute values of the negative
binding energy of a nucleus and the minimum positive energy required to
dissociate the nucleus into its
component neutrons and protons are equal.

The absolute values of the negative
neutron and proton binding energies and the positive energies to remove a
neutron or a proton, respectively, from a nucleus are equal.

The absolute values of the negative
electron binding energy and the positive energy required to remove an
electron from an
atom or molecule are equal.

Hope that
helps. Probably about half the physics students etc. are confused over the
sloppiness.